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Word equation examples:

$(x+a)^{n}=\sum_{k=0}^{n}{\binom{n}{k}x^{k}a^{n-k}}$\\


$f(x)=a_{0}+\sum_{n=1}^{\infty }{(a_{n}\cos \frac{n\pi x}{L}+b_{n}\sin 
\frac{n\pi x}{L})}$\\


$(1+x)^{n}=1+\frac{nx}{1!}+\frac{n(n-1)x^{2}}{2!}+\ldots $\\


$\sin \alpha \pm \sin \beta =2\sin \frac{1}{2}(\alpha \pm \beta )\cos 
\frac{1}{2}(\alpha \mp \beta )$\\




Fractions:

$\frac{dy}{dx}\frac{\Delta y}{\Delta x}\frac{\partial y}{\partial 
x}\frac{\delta y}{\delta x}\frac{\pi 
}{2}\frac{a}{b}\frac{c}{d}\frac{x}{y}\frac{y}{x}$\\


Scripts:

$a^{b} a_{b }a_{b}^{c}{}_{ y}{}^{x}z$\\


$x_{y^{2}}e^{-ti\theta }x^{2}{}_{1}{}^{n}Y$\\


Radicals:

$\sqrt{a}\sqrt[s]{b}\sqrt[2]{c}\sqrt[3]{x}$\\


$\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\sqrt{a^{2}+b^{2}}$\\


Integrals:

$
\int{a\int_{a}^{c}{b}}\int_{a}^{c}{b}\iint{x}\iint_{a}^{c}{x}\iint_{a}^{c}{x}\iiint{a}\iiint_{a}^{b}{x}\iiint_{a}^{b}{
\begin{gathered}
x \\
y \\
\end{gathered}
}$\\




$
\oint{x}\oint_{a}^{b}{x\oint_{a}^{b}{x\oint\oint{x\oint\oint_{a}^{b}{x\oint\oint_{a}^{b}{x}}}}}\oint\oint\oint{a}\oint\oint\oint_{b}^{c}{d}\oint\oint\oint_{e}^{f}{g}
$\\


Large operators:

$\sum_{k}{\binom{n}{k}}\sum_{i=0}^{n}{i\sum_{
\begin{gathered}
0\le i \le m \\
0<j<n \\
\end{gathered}
}{P(i,j)}\prod_{k=1}^{n}{A_{k}}}$\\


$\sum{x}\sum_{a}^{b}{c}\sum_{a}^{b}{c}\sum_{a}{b}\sum_{a}{x}$\\


$\prod{a}\prod_{b}^{c}{a}\prod_{b}^{x}{y}\prod_{a}{c}\prod_{a}{c}$\\


$
\coprod{a}\coprod_{a}^{b}{s}\coprod_{a}^{c}{s}\coprod_{a}{q}\coprod_{w}{e}
$\\


$
\bigcup{a}\bigcup_{w}^{e}{r}\bigcup_{q}^{w}{e}\bigcup_{r}{t}\bigcup_{y}{u}
$\\


$
\bigcap{s}\bigcap_{e}^{r}{t}\bigcap_{y}^{u}{i}\bigcap_{w}{e}\bigcap_{r}{t}
$\\


$
\bigvee{q}\bigvee_{e}^{r}{t}\bigvee_{y}^{u}{i}\bigvee_{o}{p}\bigvee_{a}{s}
$\\


$
\bigwedge{a}\bigwedge_{s}^{d}{f}\bigwedge_{g}^{h}{j}\bigwedge_{k}{l}\bigwedge_{z}{x}
$\\


Brackets:

$ab f(x)=\bigg\{ 
\begin{gathered}
-x, x<0 \\
x, x\ge 0 \\
\end{gathered}
\binom{n}{k}(\binom{n}{k}a\binom{n}{k}(a\frac{n}{k})a\binom{n}{k}cx$\\


$(a)\lbrack b\rbrack \lbrace c\rbrace \langle d\rangle \lfloor e\rfloor 
\lceil f\rceil \vert g\vert \Vert h\Vert \lbrack i\lbrack \rbrack 
j\rbrack \rbrack k\lbrack (l$\\


$(mn)\lbrace op\rbrace (qr(stu$\\


$(q)(w)\lbrack e(r\rbrack \lbrace t(y\rbrace \langle u(i\rangle \lfloor 
o(p\rfloor \lceil a(s\rceil \vert d(f\vert \Vert g(h\Vert (j(k)$\\


Functions:

$\bigg\{ 
\begin{gathered}
z \\
x \\
\end{gathered}
\bigg\{ 
\begin{gathered}
c \\
v \\
b \\
\end{gathered}
\binom{n}{m}\binom{q}{w}$\\


$\sin \theta \cos 2x\tan \theta =\frac{\sin \theta }{\cos \theta }$\\


$\sin q\cos w\tan e\csc r\sec t\cot y$\\


$\sin ^{-1}a\cos ^{-1}s\tan ^{-1}d\csc ^{-1}f\sec ^{-1}g\cot ^{-1}h$
\\


$\sinh z\cosh x\tanh ccsch vsech b\coth n$\\


$\sinh ^{-1}q\cosh ^{-1}w\tanh ^{-1}ecsch ^{-1}rsech ^{-1}t\coth ^{-1}y
$\\


Accents:

$\overline{A}\overline{ABC}\overline{x\oplus y}$\\


$\overline{\overline{x}+y}=x+\overline{y}$\\


$
\dot{a}\ddot{b}\dddot{c}{d}\check{e}{f}{g}\breve{h}{i}\bar{j}{k}\overbrace{l}\underbrace{m}\overbrace{n}^{o}\underbrace{p}_{q}\overleftarrow{r}\overrightarrow{ 
s}\overleftrightarrow{s t} {u}{v}\dot{abc}$\\


$aa^{2}=b^{2}+c^{2}\overline{b}\underline{c}$\\


Limit and Log:

$\lim _{n\to \infty }(1+\frac{1}{n})^{n}\max _{0\le x\le 1}xe^{-x^{2}}
$\\


$\log _{x}y\log x\lim _{a}x\min _{a}b\max _{x}y\ln z\min _{}x\max _{}y
$\\


Operators:

$\underrightarrow{yields}\underrightarrow{\Delta }$\\


$?===+=-====$\\


$
\overleftarrow{a}\overrightarrow{b}\underleftarrow{c}\underrightarrow{d}!!!DBL!!!\overleftarrow{e}!!!DBL!!!\overrightarrow{f}!!!DBL!!!\underleftarrow{g}!!!DBL!!!\underrightarrow{h}\overleftrightarrow{i}\underleftrightarrow{j}!!!DBL!!!\overleftrightarrow{k}!!!DBL!!!\underleftrightarrow{l}
$\\


$
\overleftarrow{}\overrightarrow{}\underleftarrow{}\underrightarrow{}!!!DBL!!!\overleftarrow{}!!!DBL!!!\overrightarrow{}!!!DBL!!!\underleftarrow{}!!!DBL!!!\underrightarrow{}\overleftrightarrow{}\underleftrightarrow{}!!!DBL!!!\overleftrightarrow{}!!!DBL!!!\underleftrightarrow{}
$\\




Matrices:\textbf{ }

$\begin{matrix}
a & b & \\
\end{matrix}
\begin{matrix}
a & \\
b & \\
\end{matrix}
\begin{matrix}
a & b & c & \\
\end{matrix}
\begin{matrix}
a & \\
b & \\
c & \\
\end{matrix}
\begin{matrix}
a & b & \\
c & d & \\
\end{matrix}
\begin{matrix}
a & b & c & \\
d & e & f & \\
\end{matrix}
\begin{matrix}
a & b & \\
c & d & \\
e & f & \\
\end{matrix}
\begin{matrix}
a & b & c & \\
d & e & f & \\
g & h & i & \\
\end{matrix}
$\\


$\cdots \ldots \vdots \ddots $\\


$\begin{matrix}
1 & 0 & \\
0 & 1 & \\
\end{matrix}
\begin{matrix}
1 & & \\
 & 1 & \\
\end{matrix}
\begin{matrix}
1 & 0 & 0 & \\
0 & 1 & 0 & \\
0 & 0 & 1 & \\
\end{matrix}
\begin{matrix}
1 & & & \\
 & 1 & & \\
 & & 1 & \\
\end{matrix}
$\\


$(\begin{matrix}
a & b & \\
c & d & \\
\end{matrix}
)\lbrack \begin{matrix}
a & b & \\
c & d & \\
\end{matrix}
\rbrack \vert \begin{matrix}
a & b & \\
c & d & \\
\end{matrix}
\vert \Vert \begin{matrix}
a & b & \\
c & d & \\
\end{matrix}
\Vert $\\


$(\begin{matrix}
a & \cdots & b & \\
\vdots & \ddots & \vdots & \\
c & \cdots & d & \\
\end{matrix}
)\lbrack \begin{matrix}
a & \cdots & b & \\
\vdots & \ddots & \vdots & \\
c & \cdots & d & \\
\end{matrix}
\rbrack $\\


$\lceil \begin{matrix}
 & a & & \\
 & & f & \\
z & & & \\
\end{matrix}
\rceil $\\


$\begin{matrix}
2 & 1 & 0 & 0 & \\
2 & 0 & 1 & 0 & \\
2 & 4 & 5 & 6 & \\
3 & 0 & 0 & 1 & \\
\end{matrix}
$\\




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